A173441 Number of divisors d of n such that sigma(d) divides n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 4, 1, 1, 1, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1

Offset

1,6

Comments

From Robert Israel, Oct 11 2017: (Start)

a(n) >= 1 since d=1 is always included.

a(n) = 1 if n is in A000961.

a(n) > 1 if n is in A097603. The first n not in A097603 such that a(n) > 1 is 117. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(n) - A173442(n). - A-number inserted by R. J. Mathar, Mar 06 2010

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{n>=1} 1/A009242(n) = 1.605582... . - Amiram Eldar, Mar 28 2024

Example

For n = 12, a(12) = 4; divisors of 12: 1, 2, 3, 4, 6, 12; corresponding sigma(d):1, 3, 4, 7, 12, 28; sigma(d) divides n for 4 divisors d: 1, 2, 3, 6.

Maple

f:= proc(n) nops(select(t -> n mod numtheory:-sigma(t) = 0, numtheory:-divisors(n))) end proc:
map(f, [$1..100]); # Robert Israel, Oct 11 2017

Mathematica

a[n_] := Select[Divisors[n], Divisible[n, DivisorSigma[1, #]]&] // Length;
Array[a, 100] (* Jean-François Alcover, Jun 05 2020 *)

Prog

(PARI) a(n) = sumdiv(n, d, !(n % sigma(d))); \\ Michel Marcus, Oct 11 2017

Crossrefs

Cf. A000005, A000961, A009242, A097603, A173442.

Sequence in context: A010248 A325403 A132068 * A326851 A129192 A062540

Adjacent sequences: A173438 A173439 A173440 * A173442 A173443 A173444

Keyword

nonn

Author

Jaroslav Krizek, Feb 18 2010

Status

approved